Semicircle Perimeter: Why You Must Add the Diameter

What is the perimeter of a semicircle?

The complete perimeter of a semicircle is πr + 2r, or πd/2 + d. It includes the curved half-circumference and the straight diameter. If the question asks only for the curved length, use πr instead. Decide which boundary is required before calculating.

Worked example with radius

For radius 7 cm, the curved part is 7π cm and the straight part is 14 cm. The exact perimeter is 7π + 14 cm. Using the specified approximation π ≈ 22/7 gives approximately 36 cm.

The value 22 cm would represent only the curved part under that approximation. It omits the straight edge. Tracing the outline with your finger is a simple way to catch the missing diameter.

When the diameter is given

For diameter 10 cm, first find r = 5 cm. The perimeter is 5π + 10 cm, approximately 25.7 cm using π ≈ 3.14. Inserting 10 as the radius would double every length in the answer.

Perimeter has length units such as centimetres. The area formula, πr²/2, produces square units and answers a different question. Avoid selecting a formula simply because it contains the word semicircle.

A semicircle attached to a rectangle

Suppose a semicircle of diameter 10 cm is attached along a 10 cm side of a rectangle whose other side is 8 cm. The joined diameter lies inside the shape, so it is not on the outer perimeter. The outer boundary is 8 + 8 + 10 + 5π = 26 + 5π cm, approximately 41.7 cm using π ≈ 3.14.

Practice with answers

• Radius 3 cm: full perimeter = 3π + 6 cm.
• Diameter 14 cm: curved length alone = 7π cm.
• Radius 14 cm with π ≈ 22/7: full perimeter ≈ 72 cm.

Leave answers in terms of π when an exact result is requested. Use the approximation specified by the question and avoid rounding intermediate calculations unnecessarily.

Want to check your own working? Ask a study question. AI answers require an account and paid credits. Verify important steps with your textbook or teacher.